Subgroups — C₅×D₃×#488 #14437716

Order 1920.

824 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₃×#125	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₃×#124	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#488	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5068	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5056	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×D₃×#103	C₂	1	2	yes	maximal, complemented
7	C₅×#4800	C₂	1	2	yes	maximal, complemented
8	C₅×D₃×#102	C₂	1	2	yes	maximal
9	C₅×#4768	C₂	1	2	yes	maximal, complemented
10	C₅×#4697	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₅×D₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#488	—	3	1	no	maximal, Hall
13	C₂×C₅×D₃×Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₅×D₃×D₄	C₂²	1	1	yes	characteristic
15	C₃×C₅×#125	C₂²	1	1	yes	characteristic, complemented
16	C₃×C₅×#124	C₂²	1	1	yes	characteristic
17	C₅×#947	C₂²	1	1	yes	characteristic
18	C₅×#936	C₂²	1	1	yes	characteristic
19	C₂×C₅×D₃×C₈	C₂²	1	2	yes	—
20	C₅×D₃×C₄⋊C₄	—	2	2	no	—
21	C₅×D₃×C₄⋊C₄	C₂²	1	2	yes	—
22	C₅×#890	C₂²	1	2	yes	complemented
23	C₅×#889	—	2	2	no	—
24	C₅×#885	—	2	2	no	—
25	C₅×D₃×C₂²⋊C₄	—	2	2	no	—
26	C₅×#875	C₂²	1	1	yes	characteristic
27	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
28	C₅×#870	C₂²	1	1	yes	characteristic, complemented
29	C₃×C₅×#103	C₂²	1	2	yes	complemented
30	C₃×C₅×#102	C₂²	1	2	yes	—
31	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
32	C₅×#835	C₂²	1	2	yes	complemented
33	C₅×#832	C₂²	1	2	yes	—
34	C₅×#821	C₂²	1	2	yes	—
35	C₅×#816	C₂²	1	2	yes	complemented
36	C₅×C₈×Dic₃	C₂²	1	2	yes	complemented
37	C₅×#810	C₂²	1	2	yes	complemented
38	C₅×#809	C₂²	1	2	yes	—
39	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
40	D₃×#488	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
41	C₂×C₅×#125	—	3	1	no	—
42	C₂×C₅×#124	—	3	1	no	—
43	C₅×#488	—	3	2	no	—
44	C₅×#488	—	3	2	no	—
45	C₅×#488	—	3	1	no	—
46	C₅×#488	—	3	1	no	—
47	C₅×#488	—	3	1	no	—
48	C₅×#488	D₃	1	1	yes	characteristic, direct product factor
49	C₂×C₅×#103	—	3	2	no	—
50	C₂×C₅×#102	—	3	2	no	—
51	C₂×C₄×C₅×C₈	—	3	1	no	—
52	C₂³×C₅×D₃	—	2	1	no	—
53	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
54	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
55	C₂×C₅×#67	—	2	1	no	—
56	C₅×D₃×Q₈	—	2	4	no	—
57	C₅×D₃×D₄	—	2	4	no	—
58	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
59	C₂×C₄×C₅×D₃	—	2	1	no	—
60	C₂×C₄×C₅×D₃	—	2	2	no	—
61	C₂×C₄×C₅×D₃	D₄	1	2	yes	—
62	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
63	C₂×C₅×Dic₆	—	2	1	no	—
64	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
65	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
66	C₃×C₅×C₄⋊C₄	—	2	2	no	—
67	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
68	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
69	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
70	C₅×#217	—	2	2	no	—
71	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
72	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
73	C₅×C₄⋊Dic₃	—	2	2	no	—
74	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
75	C₅×Dic₃⋊C₄	—	2	2	no	—
76	C₅×Dic₃⋊C₄	—	2	2	no	—
77	C₅×Dic₃⋊C₄	—	2	2	no	—
78	C₄×C₅×Dic₃	D₄	1	2	yes	—
79	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
80	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
81	C₅×D₃×C₈	—	2	4	no	—
82	D₃×#125	C₂×C₅	1	1	yes	characteristic, complemented
83	D₃×#124	C₂×C₅	1	1	yes	characteristic
84	C₃×#488	C₂×C₅	1	1	yes	characteristic, complemented
85	#5068	C₂×C₅	1	1	yes	characteristic, complemented
86	#5056	C₂×C₅	1	1	yes	characteristic, complemented
87	D₃×#103	C₂×C₅	1	2	yes	complemented
88	#4800	C₂×C₅	1	2	yes	complemented
89	D₃×#102	C₂×C₅	1	2	yes	—
90	#4768	C₂×C₅	1	2	yes	complemented
91	#4697	C₂×C₅	1	1	yes	characteristic, complemented
92	C₄×D₃×C₈	C₂×C₅	1	1	yes	characteristic, complemented
93	C₂²×C₅×Q₈	—	3	1	no	—
94	C₂²×C₅×D₄	—	3	1	no	—
95	C₂²×C₅×C₈	—	3	2	no	—
96	C₅×#125	—	3	2	no	—
97	C₅×#125	—	3	1	no	—
98	C₅×#125	—	6	2	no	—
99	C₅×#125	C₂×D₃	1	1	yes	characteristic, complemented
100	C₅×#124	—	3	1	no	—
101	C₅×#124	—	3	1	no	—
102	C₅×#124	—	3	1	no	—
103	C₅×#124	—	6	2	no	—
104	C₅×#124	C₂×D₃	1	1	yes	characteristic
105	C₂×C₅×C₄⋊C₄	—	3	2	no	—
106	C₂×C₅×C₄⋊C₄	—	6	2	no	—
107	C₂×C₅×C₂²⋊C₄	—	6	2	no	—
108	C₂×C₄²×C₅	—	3	1	no	—
109	C₅×#103	—	3	2	no	—
110	C₅×#103	—	3	2	no	—
111	C₅×#103	—	3	2	no	—
112	C₅×#103	C₂×D₃	1	2	yes	complemented
113	C₅×#102	—	3	2	no	—
114	C₅×#102	—	3	2	no	—
115	C₅×#102	—	3	2	no	—
116	C₅×#102	C₂×D₃	1	2	yes	—
117	C₄×C₅×C₈	—	3	2	no	—
118	C₄×C₅×C₈	—	3	1	no	—
119	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic, complemented
120	C₂×#488	—	3	1	no	Sylow
121	C₂³×C₃×C₅	—	2	1	no	—
122	C₂²×C₅×D₃	—	2	1	no	—
123	C₂²×C₅×D₃	—	4	2	no	—
124	C₂²×C₅×D₃	—	4	4	no	—
125	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
126	C₃×C₅×Q₈	—	2	2	no	—
127	C₃×C₅×D₄	—	2	2	no	—
128	C₂×C₃×C₄×C₅	—	2	2	no	—
129	C₂×C₃×C₄×C₅	—	2	1	no	—
130	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
131	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
132	C₅×#67	—	4	2	no	—
133	C₂×C₅×Dic₃	—	2	2	no	—
134	C₂×C₅×Dic₃	—	2	1	no	—
135	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
136	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
137	C₅×D₁₂	—	2	2	no	—
138	C₄×C₅×D₃	—	2	4	no	—
139	C₄×C₅×D₃	—	4	2	no	—
140	C₄×C₅×D₃	—	4	4	no	—
141	C₄×C₅×D₃	#41	1	4	yes	—
142	C₅×Dic₆	—	2	2	no	—
143	C₅×Dic₆	—	4	2	no	—
144	C₃×C₅×C₈	—	2	2	no	—
145	C₅×C₃⋊C₈	—	2	2	no	—
146	C₂×D₃×Q₈	C₂²×C₅	1	1	yes	characteristic
147	C₂×D₃×D₄	C₂²×C₅	1	1	yes	characteristic
148	C₃×#125	C₂²×C₅	1	1	yes	characteristic, complemented
149	C₃×#124	C₂²×C₅	1	1	yes	characteristic
150	#947	C₂²×C₅	1	1	yes	characteristic
151	#936	C₂²×C₅	1	1	yes	characteristic
152	C₂×D₃×C₈	C₂²×C₅	1	2	yes	—
153	D₃×C₄⋊C₄	—	2	2	no	—
154	D₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
155	#890	C₂²×C₅	1	2	yes	complemented
156	#889	—	2	2	no	—
157	#885	—	2	2	no	—
158	D₃×C₂²⋊C₄	—	2	2	no	—
159	#875	C₂²×C₅	1	1	yes	characteristic
160	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
161	#870	C₂²×C₅	1	1	yes	characteristic, complemented
162	C₃×#103	C₂²×C₅	1	2	yes	complemented
163	C₃×#102	C₂²×C₅	1	2	yes	—
164	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
165	#835	C₂²×C₅	1	2	yes	complemented
166	#832	C₂²×C₅	1	2	yes	—
167	#821	C₂²×C₅	1	2	yes	—
168	#816	C₂²×C₅	1	2	yes	complemented
169	C₈×Dic₃	C₂²×C₅	1	2	yes	complemented
170	#810	C₂²×C₅	1	2	yes	complemented
171	#809	C₂²×C₅	1	2	yes	—
172	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
173	C₂⁴×C₅	—	6	1	no	—
174	C₂×C₅×Q₈	—	3	1	no	—
175	C₂×C₅×Q₈	—	6	1	no	—
176	C₂×C₅×Q₈	—	6	4	no	—
177	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
178	C₂×C₅×D₄	—	3	1	no	—
179	C₂×C₅×D₄	—	6	4	no	—
180	C₂×C₅×D₄	—	6	1	no	—
181	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
182	C₂²×C₄×C₅	—	3	1	no	—
183	C₂²×C₄×C₅	—	3	2	no	—
184	C₂²×C₄×C₅	—	6	1	no	—
185	C₂²×C₄×C₅	—	6	2	no	—
186	C₂×C₅×C₈	—	3	2	no	—
187	C₂×C₅×C₈	—	6	4	no	—
188	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
189	C₅×C₄⋊C₄	—	2	2	no	—
190	C₅×C₄⋊C₄	—	3	2	no	—
191	C₅×C₄⋊C₄	—	6	2	no	—
192	C₅×C₄⋊C₄	—	6	2	no	—
193	C₅×C₄⋊C₄	—	6	2	no	—
194	C₅×C₄⋊C₄	—	6	2	no	—
195	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
196	C₅×C₂²⋊C₄	—	2	2	no	—
197	C₅×C₂²⋊C₄	—	6	2	no	—
198	C₅×C₂²⋊C₄	—	6	2	no	—
199	C₅×C₂²⋊C₄	—	6	2	no	—
200	C₄²×C₅	—	3	2	no	—
201	C₄²×C₅	—	3	1	no	—
202	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
203	C₂×#125	—	3	1	no	—
204	C₂×#124	—	3	1	no	—
205	#488	—	3	1	no	—
206	#488	—	3	1	no	—
207	#488	—	3	2	no	—
208	#488	—	3	2	no	—
209	#488	—	3	1	no	—
210	#488	C₅×D₃	1	1	yes	characteristic, direct product factor
211	C₂×#103	—	3	2	no	—
212	C₂×#102	—	3	2	no	—
213	C₂×C₄×C₈	—	3	1	no	—
214	C₂²×C₃×C₅	—	4	1	no	—
215	C₂²×C₃×C₅	—	4	2	no	—
216	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₅×D₃	—	4	1	no	—
218	C₂×C₅×D₃	—	4	2	no	—
219	C₂×C₅×D₃	—	8	4	no	—
220	C₂×C₅×D₃	#124	1	2	yes	—
221	C₂×C₅×D₃	#135	1	4	yes	—
222	C₃×C₄×C₅	—	2	2	no	—
223	C₃×C₄×C₅	—	4	1	no	—
224	C₃×C₄×C₅	—	4	2	no	—
225	C₃×C₄×C₅	C₂×#41	1	2	yes	—
226	C₅×Dic₃	—	2	2	no	—
227	C₅×Dic₃	—	4	1	no	—
228	C₅×Dic₃	—	4	2	no	—
229	C₅×Dic₃	#124	1	2	yes	—
230	C₂³×D₃	—	2	1	no	—
231	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
232	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
233	C₂×#67	—	2	1	no	—
234	D₃×Q₈	—	2	4	no	—
235	D₃×D₄	—	2	4	no	—
236	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
237	C₂×C₄×D₃	—	2	1	no	—
238	C₂×C₄×D₃	—	2	2	no	—
239	C₂×C₄×D₃	C₅×D₄	1	2	yes	—
240	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
241	C₂×Dic₆	—	2	1	no	—
242	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
243	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
244	C₃×C₄⋊C₄	—	2	2	no	—
245	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
246	C₃×C₂²⋊C₄	—	2	2	no	—
247	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
248	#217	—	2	2	no	—
249	(C₂×D₃)⋊C₄	—	2	2	no	—
250	(C₂×D₃)⋊C₄	—	2	2	no	—
251	C₄⋊Dic₃	—	2	2	no	—
252	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
253	Dic₃⋊C₄	—	2	2	no	—
254	Dic₃⋊C₄	—	2	2	no	—
255	Dic₃⋊C₄	—	2	2	no	—
256	C₄×Dic₃	C₅×D₄	1	2	yes	—
257	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
258	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
259	D₃×C₈	—	2	4	no	—
260	C₂³×C₅	—	2	1	no	—
261	C₂³×C₅	—	3	1	no	—
262	C₂³×C₅	—	6	1	no	—
263	C₂³×C₅	—	12	2	no	—
264	C₂³×C₅	—	12	4	no	—
265	C₅×Q₈	—	2	2	no	—
266	C₅×Q₈	—	6	2	no	—
267	C₅×Q₈	—	12	2	no	—
268	C₅×D₄	—	2	2	no	—
269	C₅×D₄	—	6	2	no	—
270	C₅×D₄	—	12	2	no	—
271	C₂×C₄×C₅	—	2	1	no	—
272	C₂×C₄×C₅	—	2	2	no	—
273	C₂×C₄×C₅	—	3	1	no	—
274	C₂×C₄×C₅	—	3	4	no	—
275	C₂×C₄×C₅	—	3	2	no	—
276	C₂×C₄×C₅	—	6	4	no	—
277	C₂×C₄×C₅	—	6	1	no	—
278	C₂×C₄×C₅	—	6	2	no	—
279	C₂×C₄×C₅	—	12	4	no	—
280	C₂×C₄×C₅	—	12	2	no	—
281	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
282	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
283	C₅×C₈	—	2	2	no	—
284	C₅×C₈	—	6	2	no	—
285	C₂²×Q₈	—	3	1	no	—
286	C₂²×D₄	—	3	1	no	—
287	C₂²×C₈	—	3	2	no	—
288	#125	—	3	2	no	—
289	#125	—	3	1	no	—
290	#125	—	6	2	no	—
291	#125	C₂×C₅×D₃	1	1	yes	characteristic, complemented
292	#124	—	3	1	no	—
293	#124	—	3	1	no	—
294	#124	—	3	1	no	—
295	#124	—	6	2	no	—
296	#124	C₂×C₅×D₃	1	1	yes	characteristic
297	C₂×C₄⋊C₄	—	3	2	no	—
298	C₂×C₄⋊C₄	—	6	2	no	—
299	C₂×C₂²⋊C₄	—	6	2	no	—
300	C₂×C₄²	—	3	1	no	—
301	#103	—	3	2	no	—
302	#103	—	3	2	no	—
303	#103	—	3	2	no	—
304	#103	C₂×C₅×D₃	1	2	yes	complemented
305	#102	—	3	2	no	—
306	#102	—	3	2	no	—
307	#102	—	3	2	no	—
308	#102	C₂×C₅×D₃	1	2	yes	—
309	C₄×C₈	—	3	2	no	—
310	C₄×C₈	—	3	1	no	—
311	C₄×C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
312	C₂×C₃×C₅	—	8	1	no	—
313	C₂×C₃×C₅	C₂×#124	1	1	yes	characteristic
314	C₂×C₃×C₅	C₂×#135	1	2	yes	—
315	C₅×D₃	—	8	1	no	—
316	C₅×D₃	#488	1	4	yes	direct product factor
317	C₂³×C₃	—	2	1	no	—
318	C₂²×D₃	—	2	1	no	—
319	C₂²×D₃	—	4	2	no	—
320	C₂²×D₃	—	4	4	no	—
321	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
322	C₃×Q₈	—	2	2	no	—
323	C₃×D₄	—	2	2	no	—
324	C₂×C₃×C₄	—	2	2	no	—
325	C₂×C₃×C₄	—	2	1	no	—
326	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
327	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
328	#67	—	4	2	no	—
329	C₂×Dic₃	—	2	2	no	—
330	C₂×Dic₃	—	2	1	no	—
331	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
332	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
333	D₁₂	—	2	2	no	—
334	C₄×D₃	—	2	4	no	—
335	C₄×D₃	—	4	2	no	—
336	C₄×D₃	—	4	4	no	—
337	C₄×D₃	C₅×#41	1	4	yes	—
338	Dic₆	—	2	2	no	—
339	Dic₆	—	4	2	no	—
340	C₃×C₈	—	2	2	no	—
341	C₃⋊C₈	—	2	2	no	—
342	C₂²×C₅	—	3	2	no	—
343	C₂²×C₅	—	3	4	no	—
344	C₂²×C₅	—	4	1	no	—
345	C₂²×C₅	—	4	2	no	—
346	C₂²×C₅	—	12	1	no	—
347	C₂²×C₅	—	12	2	no	—
348	C₂²×C₅	—	24	4	no	—
349	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
350	C₄×C₅	—	2	2	no	—
351	C₄×C₅	—	3	2	no	—
352	C₄×C₅	—	4	1	no	—
353	C₄×C₅	—	4	2	no	—
354	C₄×C₅	—	6	2	no	—
355	C₄×C₅	—	12	1	no	—
356	C₄×C₅	—	12	2	no	—
357	C₄×C₅	D₃×#41	1	2	yes	—
358	C₂⁴	—	6	1	no	—
359	C₂×Q₈	—	3	1	no	—
360	C₂×Q₈	—	6	1	no	—
361	C₂×Q₈	—	6	4	no	—
362	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
363	C₂×D₄	—	3	1	no	—
364	C₂×D₄	—	6	4	no	—
365	C₂×D₄	—	6	1	no	—
366	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
367	C₂²×C₄	—	3	1	no	—
368	C₂²×C₄	—	3	2	no	—
369	C₂²×C₄	—	6	1	no	—
370	C₂²×C₄	—	6	2	no	—
371	C₂×C₈	—	3	2	no	—
372	C₂×C₈	—	6	4	no	—
373	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	3	2	no	—
376	C₄⋊C₄	—	6	2	no	—
377	C₄⋊C₄	—	6	2	no	—
378	C₄⋊C₄	—	6	2	no	—
379	C₄⋊C₄	—	6	2	no	—
380	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
381	C₂²⋊C₄	—	2	2	no	—
382	C₂²⋊C₄	—	6	2	no	—
383	C₂²⋊C₄	—	6	2	no	—
384	C₂²⋊C₄	—	6	2	no	—
385	C₄²	—	3	2	no	—
386	C₄²	—	3	1	no	—
387	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
388	C₃×C₅	C₂×#488	1	1	yes	characteristic, complemented, Hall
389	C₂²×C₃	—	4	1	no	—
390	C₂²×C₃	—	4	2	no	—
391	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
392	C₂×D₃	—	4	1	no	—
393	C₂×D₃	—	4	2	no	—
394	C₂×D₃	—	8	4	no	—
395	C₂×D₃	C₅×#124	1	2	yes	—
396	C₂×D₃	C₅×#135	1	4	yes	—
397	C₃×C₄	—	2	2	no	—
398	C₃×C₄	—	4	1	no	—
399	C₃×C₄	—	4	2	no	—
400	C₃×C₄	C₂×C₅×#41	1	2	yes	—
401	Dic₃	—	2	2	no	—
402	Dic₃	—	4	1	no	—
403	Dic₃	—	4	2	no	—
404	Dic₃	C₅×#124	1	2	yes	—
405	C₂×C₅	—	3	4	no	—
406	C₂×C₅	—	8	1	no	—
407	C₂×C₅	—	24	1	no	—
408	C₂×C₅	D₃×#124	1	1	yes	characteristic
409	C₂×C₅	D₃×#135	1	2	yes	—
410	C₂³	—	2	1	no	—
411	C₂³	—	3	1	no	—
412	C₂³	—	6	1	no	—
413	C₂³	—	12	2	no	—
414	C₂³	—	12	4	no	—
415	Q₈	—	2	2	no	—
416	Q₈	—	6	2	no	—
417	Q₈	—	12	2	no	—
418	D₄	—	2	2	no	—
419	D₄	—	6	2	no	—
420	D₄	—	12	2	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	3	1	no	—
424	C₂×C₄	—	3	4	no	—
425	C₂×C₄	—	3	2	no	—
426	C₂×C₄	—	6	4	no	—
427	C₂×C₄	—	6	1	no	—
428	C₂×C₄	—	6	2	no	—
429	C₂×C₄	—	12	2	no	—
430	C₂×C₄	—	12	4	no	—
431	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
432	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
433	C₈	—	2	2	no	—
434	C₈	—	6	2	no	—
435	C₂×C₃	—	8	1	no	—
436	C₂×C₃	C₂×C₅×#124	1	1	yes	characteristic
437	C₂×C₃	C₂×C₅×#135	1	2	yes	—
438	D₃	—	8	1	no	—
439	D₃	C₅×#488	1	4	yes	direct product factor
440	C₅	D₃×#488	1	1	yes	characteristic, direct product factor, Sylow
441	C₂²	—	3	2	no	—
442	C₂²	—	3	4	no	—
443	C₂²	—	4	1	no	—
444	C₂²	—	4	2	no	—
445	C₂²	—	12	1	no	—
446	C₂²	—	12	2	no	—
447	C₂²	—	24	4	no	—
448	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
449	C₄	—	2	2	no	—
450	C₄	—	3	2	no	—
451	C₄	—	4	1	no	—
452	C₄	—	4	2	no	—
453	C₄	—	6	2	no	—
454	C₄	—	12	1	no	—
455	C₄	—	12	2	no	—
456	C₄	C₅×D₃×#41	1	2	yes	—
457	C₃	C₂×C₅×#488	1	1	yes	characteristic, complemented, Sylow
458	C₂	—	3	4	no	—
459	C₂	—	8	1	no	—
460	C₂	—	24	1	no	—
461	C₂	C₅×D₃×#124	1	1	yes	characteristic
462	C₂	C₅×D₃×#135	1	2	yes	—

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#488	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₅×D₃×D₄	C₂²
hypercenter	C₅×#488	D₃
hypocenter	C₃	C₂×C₅×#488
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#488

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₅×D₃×#125	C₂	semidirect
3. C₃×C₅×#488	C₂	semidirect
4. C₅×#5068	C₂	semidirect
5. C₅×#5056	C₂	semidirect
6. C₅×D₃×#103	C₂	semidirect
7. C₅×#4800	C₂	semidirect
9. C₅×#4768	C₂	semidirect
10. C₅×#4697	C₂	semidirect
11. C₄×C₅×D₃×C₈	C₂	semidirect
15. C₃×C₅×#125	C₂²	semidirect
22. C₅×#890	C₂²	semidirect
28. C₅×#870	C₂²	semidirect
29. C₃×C₅×#103	C₂²	semidirect
31. C₃×C₄×C₅×C₈	C₂²	semidirect
32. C₅×#835	C₂²	semidirect
35. C₅×#816	C₂²	semidirect
36. C₅×C₈×Dic₃	C₂²	semidirect
37. C₅×#810	C₂²	semidirect
39. C₄×C₅×C₃⋊C₈	C₂²	semidirect
40. D₃×#488	C₅	direct (N × H)
48. C₅×#488	D₃	direct (N × H)
82. D₃×#125	C₂×C₅	semidirect
84. C₃×#488	C₂×C₅	semidirect
85. #5068	C₂×C₅	semidirect
86. #5056	C₂×C₅	semidirect
87. D₃×#103	C₂×C₅	semidirect
88. #4800	C₂×C₅	semidirect
90. #4768	C₂×C₅	semidirect
91. #4697	C₂×C₅	semidirect
92. C₄×D₃×C₈	C₂×C₅	semidirect
99. C₅×#125	C₂×D₃	semidirect
112. C₅×#103	C₂×D₃	semidirect
119. C₄×C₅×C₈	C₂×D₃	semidirect
148. C₃×#125	C₂²×C₅	semidirect
155. #890	C₂²×C₅	semidirect
161. #870	C₂²×C₅	semidirect
162. C₃×#103	C₂²×C₅	semidirect
164. C₃×C₄×C₈	C₂²×C₅	semidirect
165. #835	C₂²×C₅	semidirect
168. #816	C₂²×C₅	semidirect
169. C₈×Dic₃	C₂²×C₅	semidirect
170. #810	C₂²×C₅	semidirect
172. C₄×C₃⋊C₈	C₂²×C₅	semidirect
210. #488	C₅×D₃	direct (N × H)
291. #125	C₂×C₅×D₃	semidirect
304. #103	C₂×C₅×D₃	semidirect
311. C₄×C₈	C₂×C₅×D₃	semidirect
316. C₅×D₃	#488	direct (N × H)
388. C₃×C₅	C₂×#488	semidirect
439. D₃	C₅×#488	direct (N × H)
440. C₅	D₃×#488	direct (N × H)
457. C₃	C₂×C₅×#488	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅×D₃×#125	2
C₅×D₃×#124	2
C₃×C₅×#488	2
C₅×#5068	2
C₅×#5056	2
C₅×D₃×#103	2
C₅×#4800	2
C₅×D₃×#102	2
C₅×#4768	2
C₅×#4697	2
C₄×C₅×D₃×C₈	2
C₂×C₅×#488	3
D₃×#488	5

Subgroups — C5×D3×#488 #14437716

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#488 #14437716